Quasicrystal
structure based on the golden mean won Daniel Shechtman the 2011 Nobel Prize in
Chemistry; Dr. Mae-Wan Ho finds
out why it is a thing of beauty

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Daniel Shectman with quasicrystal
icosahedron

Dan Shechtman
looked down the electron microscope on the morning of 8 April 1982 and saw the crystal
structure of an aluminium and manganese alloy (Al_{6}Mn) that he had
created. It was impossible! He could not believe the structure could exist. A
later diffraction pattern obtained with a larger crystal under X-ray showed
concentric circles, each with ten bright dots that were equidistant from its
neighbours (Figure 1) [1, 2]. He had rapidly chilled the molten metal, and
expected the sudden change in temperature to have created complete disorder.
Instead, there was order of a different kind from any crystal previously known
to exist. He had created a new kind of ordered structure called a quasicrystal.
But it took quite a while for the scientific community to accept his finding.

Figure 1 Diffraction pattern of Dan
Shechtman’s crystal (left) and how it was obtained

“I told everyone who was ready to listen that
I had material with pentagonal symmetry. People just laughed at me,” Shechtman
recalls when interviewed in his office at the Israel Institute of Technology, Haifa, Israel, surrounded by numerous prizes he has won before the crowning glory of the
Nobel award [3].

In fact, Shectman lost his job soon after his
discovery. Linus Pauling accused him of “talking nonsense”, and delivered the
ultimate insult [4]: “There is no such thing as quasicrystals, only quasiscientists.”

Quasicrystals a
new kind of solids

A quasicrystal
is an ordered structure that is not periodic. It can continuously fill all
available space, but it lacks translational symmetry, which means that an
arbitrary part of it cannot be shifted from its original position to another
place without destroying the symmetry. While crystals, according to the
classical ‘crystallographic restriction theorem’, can possess only two, three,
four, and six-fold symmetries, quasicrystals show other symmetry orders, for
instance five-fold.

Paul J.
Steinhardt, professor of physics at Princeton University, New Jersey, in the United States defines quasicrytals more precisely as quasiperiodic structures with
forbidden symmetry that can be reduced to a finite number of repeating units
[2]. These structures were inspired by Penrose tilings in two dimensions.

Aperiodic
tilings were discovered by mathematicians in the early 1960s. In 1972, Roger
Penrose created a two-dimensional tiling pattern with only two different pieces
that was not periodic and had a five-fold symmetry (see Figure 2).

Figure 2 Penrose tilings from John Steinhardt with 5, 7 and 11-fold symmetries (left to right) [2]

Quasicrystals
are higher dimensions Penrose tiling (and obey rules other than what Penrose
had discovered). They are a new class of solids not just with 5-fold symmetry,
but any symmetry in any number of dimensions [2]. This includes a dynamic icosahedron
quasicrystal structure of 280 molecules of water discovered by Martin Chaplin
at South Bank University, London, in the UK [5, 6] (see Two-States Water
Explains All?SiS 32).

Quasicrystals
and the golden mean

An intriguing
feature of quasicrystals is that the mathematical ‘irrational’ constant (irrational
because it cannot be expressed as a fraction) known as the Greek letter j, or the “golden
ratio” is embedded in the structure [5, 7], which in turn underlies a number sequence
worked out by Fibonacci in the 13th century, where each number is the sum of
the preceding two.

Two
quantities are in the golden ratio if the ratio of the sum of the quantities to
the larger quantity is equal to the ratio of the larger quantity to the smaller
one. The golden ratio is approximately 1.61803398874989. Other names frequently
used for the golden ratio are the golden proportion, the golden section, or
golden mean.

The
Fibonacci sequence is a sequence of numbers, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55,
89, 144, ….., where the ratio of a number in the sequence to the previous
approaches j asymptotically, i.e., more and more exactly as the numbers get
larger and larger.

The
golden mean was the Greek ideal of beauty and harmony, and had a tremendous
influence on architecture, art and design.

It
is significant that quasicrystals do represent minimum energy structures [2, 5],
and hence a kind of frozen equilibrium between harmony and tension in just the
right degree, which may be where beauty lies.

Sibylle Gabriel Comment left 7th November 2011 21:09:36 It is where beauty lies and I am very happy that we are slowly coming to the truth.

Todd Millions Comment left 20th November 2011 08:08:05 Synergetics II by Buckminister Fuller-the illistration for 'strut bonded tensigrity Icosa's,'with the -'bow tie voids' between them.
Thus were quasi crystals predicted,and one could predict certian features not yet noticed in the original pictures.
So far as I've ever known,I was the only one too notice this.

yezude Comment left 15th June 2013 15:03:38 golden section is the organisation of this universe

MSalahE Comment left 27th October 2014 07:07:14 Scholarly articles for el naschie and thooft Elementary ...
https://plus.google.com/.../posts/g96Nx7uTonW
Mohamed El Naschie
5 days ago - Scholarly articles for el naschie and thooft. Elementary prerequisites for< i> E-infinity:( … - El Naschie - Cited by 155 … Kähler manifolds, Klein modular space ...
Scholarly articles for el naschie and thooft Elementary ...
https://plus.google.com/.../posts/hjwW46mLFLR
Mohamed El Naschie
5 days ago - Scholarly articles for el naschie and thooft. Elementary prerequisites for< i> E-infinity:( … - El Naschie - Cited by 155 … Kähler manifolds, Klein modular space ...

assem deif Comment left 13th October 2016 13:01:37 3 comments:
1. The golden section is not the Greek ideal of beauty. It was mentioned in Euclid book "the elements". Euclid origin is unknown. Smith called him Euclid of Alexandria. Many Egyptians were given Greek names. Ptolemy the astronomer is from upper Egypt, so is Eratostenes from Salloom. I have a Muslim friend who is an Egyptian peasant who called his daughter Nancy. I am sure she is not American
2. Much earlier than Euclid many Egyptian monuments carry these proportions as was documented by the Egyptologist Shwaller de Lubic
3. Fibonacci sequence not necessarily 1,1,2,3,5,... you can start with any 2 numbers 5,2,7,9,16,... the ratio of 2 consecutive no's tend to phi